Using the following regression table, we can see that the assumed lineas rogression is significant at 0.05 level of significance Regression Statistics Multiple R R Square Adjusted R Square Standard 2.54008 Observati 79 ANOVA Regressio Residual Total df Select one: True O False SS MS gnificance F 1 8241.992 8241.992 1277.430962 1.06E-49 77 496.8045 6.452006 78 8738.797 Coefficientandard Err t Stat P-value Lower 95%Upper 95%ower 95.0%pper 95.0% 13.2083 10.91027 13.2083 Intercept 12.05928 0.577032 20.8988 0.008080197 10.91027 0.44792 0.012532 35.74117 0.063939553 0.422965 0.472876 0.422965 0.472876
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- Which of the following assumptions is not necessary for unbiasedness of a slope coefficient in a multiple regression model? MLR1 MLR 4 Homoskedasticity Random samplingThe following data is a regression model where the U.S. Department of Transportation has tried to relate the rate of fatal traffic accidents (per 1000 licenses) to the percentage of motorists under the age of 21. Data has been collected for 42 major cities in the United States. SUMMARY OUTPUT Regression Statistics Multiple R 0.83938748 R Square 0.70457134 Adjusted R Square 0.69718562 Standard Error 0.58935028 Observations 42 ANOVA df SS MS F Regression 1 33.13441764 33.1344 95.3964 Residual 40 13.89335048 0.34733 Total 41 47.02776812 Coefficients Standard Error t Stat P-value Intercept -1.5974138 0.371671454 -4.2979 0.00010 Percent Under 21 0.28705317 0.029389769 9.76711 3.79E-9…For a bivariate regression, the assessment of effect size is determined by Pearson’s r. Group of answer choices True False
- A part of the output of a regression analysis of Y against X using Excel is given below:SUMMARY OUTPUTRegression StatisticsMultiple R 0.954704R Square 0.91146Adjusted R Square 0.896703Standard Error 28.98954Observations 8ANOVAdf SS MS F Significance FRegression 1 51907.64 51907.64Residual 6 5042.361 840.3936Total 7 56950Coefficients Standard Error t Stat P-valueIntercept 45.2159 39.8049Age 5.3265 0.6777a. State the estimated regression line and interpret the slope coefficient.Consider the following computer output of a multiple regression analysis relating annual salary to years of education and years of work experience. Regression Statistics Multiple R 0.73520.7352 R Square 0.54050.5405 Adjusted R Square 0.52050.5205 Standard Error 2131.18202131.1820 Observations 4949 ANOVA dfdf SSSS MSMS F� Significance F� Regression 22 245,793,126.4218245,793,126.4218 122,896,563.2109122,896,563.2109 27.058227.0582 1.7E-081.7E-08 Residual 4646 208,929,085.5374208,929,085.5374 4,541,936.64214,541,936.6421 Total 4848 454,722,211.9592454,722,211.9592 Coefficients Standard Error t� Stat P-value Lower 95%95% Upper 95%95% Intercept 14268.6823614268.68236 2,521.08442,521.0844 5.65975.6597 0.0000009340.000000934 9194.00279194.0027 19,343.362119,343.3621 Education (Years) 2352.26982352.2698 337.1115337.1115 6.97776.9777 0.000000010.00000001 1673.69951673.6995 3030.84013030.8401 Experience (Years) 832.2096832.2096…Calculate the R2of the following multivariate sample regression functions and interpret theanswers.3.1 Investment-hat = β1-hat + β2-hat*Interest rate + β3-hat*Exchange rateESS = 900RSS = 1003.2 Investment-hat = β1 + β2-hat*Interest rate + β3-hat*number of 311 studentsESS = 400RSS = 6003.3 Salary-hat = β1 + β2-hat*Frequency of blinking eyes + β3-hat*Colour of hairRSS = 950TSS = 1000
- Consider the following computer output of a multiple regression analysis relating annual salary to years of education and years of work experience. Regression Statistics Multiple R 0.73720.7372 R Square 0.54340.5434 Adjusted R Square 0.52350.5235 Standard Error 2120.66062120.6606 Observations 4949 ANOVA dfdf SSSS MSMS F� Significance F� Regression 22 246,191,336.3605246,191,336.3605 123,095,668.1803123,095,668.1803 27.371627.3716 1.5E-081.5E-08 Residual 4646 206,871,255.7619206,871,255.7619 4,497,201.21224,497,201.2122 Total 4848 453,062,592.1224453,062,592.1224 Coefficients Standard Error t� Stat P-value Lower 95%95% Upper 95%95% Intercept 14262.1701214262.17012 2,508.63812,508.6381 5.68525.6852 0.0000008560.000000856 9212.54359212.5435 19,311.796719,311.7967 Education (Years) 2354.97312354.9731 335.4472335.4472 7.02047.0204 0.0000000080.000000008 1679.75291679.7529 3030.19333030.1933 Experience (Years) 830.0759830.0759…Consider the following computer output of a multiple regression analysis relating annual salary to years of education and years of work experience. Regression Statistics Multiple R 0.73720.7372 R Square 0.54340.5434 Adjusted R Square 0.52350.5235 Standard Error 2120.66062120.6606 Observations 4949 ANOVA dfdf SSSS MSMS F� Significance F� Regression 22 246,191,336.3605246,191,336.3605 123,095,668.1803123,095,668.1803 27.371627.3716 1.5E-081.5E-08 Residual 4646 206,871,255.7619206,871,255.7619 4,497,201.21224,497,201.2122 Total 4848 453,062,592.1224453,062,592.1224 Coefficients Standard Error t� Stat P-value Lower 95%95% Upper 95%95% Intercept 14262.1701214262.17012 2,508.63812,508.6381 5.68525.6852 0.0000008560.000000856 9212.54359212.5435 19,311.796719,311.7967 Education (Years) 2354.97312354.9731 335.4472335.4472 7.02047.0204 0.0000000080.000000008 1679.75291679.7529 3030.19333030.1933 Experience (Years) 830.0759830.0759…Consider the following computer output from a multiple regression analysis relating the price of a used car to the variables: age of car, mileage, and safety rating. Coefficients Coefficients Standard Error t� Stat P-value Intercept 42465.6942465.69 5320.545320.54 7.9817.981 0.00000.0000 Age (Year) −21096.02−21096.02 2551.522551.52 −8.268−8.268 0.00000.0000 Mileage(in Thousands) −1312.73−1312.73 103.02103.02 −12.743−12.743 0.00000.0000 Safety Rating 1533.821533.82 165.72165.72 9.2559.255 0.00000.0000 Does the sign of the coefficient for the variable safety rating make sense?
- Consider the following summary from from a simple linear regression involving a very small data set of n = 5 observations. Coefficients: Estimate Std. Error Intercept 9.8758 0.4882 Slope 0.5704 0.7287 Suppose all of our usual regression assumptions are met. If we wish to test the null hypothesis that there is no linear relationship between X and Y, what is the value of the appropriate t test statistic? (Give your numeric response to 3 decimal places. Give only your numeric response, and not any extra characters or symbols.)If the standard error of the estimate for a regression model fitted to a large number of paired observations is 1.75, approximately 95% of the residuals would lie within ______. −3.50 and +3.50 −1.75 and +1.75 −0.95 and +0.95 −0.68 and +0.68 −0.97 and +0.97The Following data is given for the period 1999-2003 Interest rate Inflation i π 1999 4.7 4.4 2000 4.6 5.4 2001 6.3 5.7 2002 4.8 4.6 2003 2.9 2.4 Obtain residuals of the regression. Calculate variance of the residuals and the standard errors of the parameters